Smart Starters · Ages 8 to 10
Area Model Multiplication 2 by 2
Two-digit by two-digit multiplication using an area model. Five levels with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Area Model Multiplication 2 by 2
When both numbers in a multiplication are partitioned, the result is four products rather than two, and the area model is the picture that keeps track of them. Twenty-three times forty-five becomes a rectangle split into four smaller rectangles — twenty by forty, twenty by five, three by forty, three by five — and the total area is the answer. This is the grid method one step further on, and it is the last representation before the compact algorithm, so it is worth getting solidly. Each question prints the rectangle with both partitions marked along its edges and the four regions empty, which is what makes a missing product visible; a child who fills three cells and stops can see the gap. Both factors are always genuinely two-digit with a non-zero ones digit, so all four regions are real — a number ending in zero would collapse the model to two products and teach the wrong shape. The numbers grow across the levels while the four-region structure stays fixed. A ruled line beneath each model collects the total. Its on-screen twin is Area Model Multiply Studio.
Common questions
- Why are there four products?
- Both numbers are partitioned, so the rectangle splits into four smaller ones. Their total area is the answer.
- Could a region be missing?
- No. Both factors always have a non-zero ones digit, so all four regions are real.
- How does this relate to the grid method?
- It is the same idea one step further on — the last representation before the compact algorithm.
- Is an answer key included?
- Yes. Every level downloads with its own separate answer key PDF.
A hand for grown-ups
- Before you start
- Think of it as groups: "4 × 3" is four groups of three. Have something you can arrange into equal groups.
- While they work
- Skip-counting (3, 6, 9, 12…) is a solid way in before facts are memorised. Let them use it — speed comes later.
- Afterwards
- Spot arrays in real life together — eggs in a box, tiles on a floor. Rows-and-columns is multiplication you can see.
- Watch out for
- Treating it as harder addition and losing track. Grouping objects physically keeps the "equal groups" idea in view.
- Away from the screen
- Lay out objects in rows and columns and count them two ways. Cooking with doubled recipes is multiplication too.
Where to go next
Chosen by the skills this activity practises.